m 



i LIBRARY OF CONGRESS.! 

#|''-i? feright ^0 , ^j 

#• (7^^// 0\C\ # ' 



I UNITED STATES OF AMERICA. 



TJk.BLES 



SHOWING 

DIFFERENCES OF LEVEL 

IN FEET, 

CORRESPONDING TO A GIVEN ANGLE, 

WHEN THE DISTANCE IS READ 

IN METRES, 



HORIZONTAL REDUCTIONS, 

FOB^USE WITH STADIA. 



COMPUTED BY . ^$U!^^, X 

J. A. OCKERSOK § JARED TEEPLE, 

Ass^t Eng'rs U. S. Lake Survey^ 



Entered according to Act of Congress in the year 1875, ^X 

J. A. OCKERSON and JARED TEEPLE, 

In the Office of the Librarian of Congress at Washington. 






c^M^^ 



NOTE 



The following formulae, deduced by Professor 
S. W. Robinson, of the Illinois Industrial Univer- 
sity, were used in the computation of these tables. 

R' 

H=—{^B — c—f)sm.2V-^{c-\-f')sm. V 

2R 

R' 

D=^ {B —c — /) cos,-" /^ + ( ^ +/) COS. V, 
R 

R' = any reading of the stadia. 

B = length of a measured base. 

R^=^ reading of stadia on the base. 

F= angle of elevation or depression. 

c = distance from centre of instrument to centre 
of object glass. 

f^=i principal focal length of object glass. 

(^+/) = 0.43 metres. 

H 1= difference of level. 

D = horizontal distance. 

When Fand R^ are known, the value of ZTmay 
be taken from the tables as follows : 

Required the difference of level when F=i2^ 
30' and ^' = 410 metres. 

In the column headed 410 and opposit9 2° 30', 
we find 58.6 feet, which is the difference of level 
required. 



If Vis the same as before and ^' ^ 418 metres, 
we would have, as the column headed Z) gives the 
difference for one metre, 

JI= 58.6 + 8 X . 143 = 59-7 feet. 

The table on page 19 will give the difference of 
level in feet by multiplying the difference for the 
given angle by the distance in metres. 

Example. — The difference for 2° 30' from table 
is .1428, which multiplied by 418 gives 59.7, the 
same as above. 

HORIZONTAL REDUCTIONS. 

Page 20 contains a table for use in obtaining the 
horizontal distance for any stadia reading, having an 
elevation less than 20°. 

Example — Required the reduction when V:=: 
7° 42' and i?' = 368 metres. 

From the column headed 7° and opposite 42', we 
find .0180, which multiplied by 368 gives 6.624, the 
reduction required, and the horizontal distance 
= 368 — 6.624 = 361.376. 



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